Dra. Rodríguez-Durán, Evelyn

In this work we obtain known and new supersymmetric extensions of diverse asymptotic symmetries defined in three spacetime dimensions by considering the semigroup expansion method. The super-BMS3, the superconformal algebra and new infinite-dimensional superalgebras are obtained by expanding the super-Virasoro algebra. The new superalgebras obtained are supersymmetric extensions of the asymptotic algebras of the Maxwell and the so(2, 2)⊕ so(2, 1) gravity theories. We extend our results to the N = 2 and N = 4 cases and find that R-symmetry generators are required. We also show that the new infinite-dimensional structures are related through a flat limit → ∞.

We present a novel three-dimensional non-relativistic Chern-Simons supergravity theory invariant under a Maxwellian extended Bargmann superalgebra. We first study the non-relativistic limits of the minimal and the N = 2 Maxwell superalgebras. We show that a well-defined Maxwellian extended Bargmann supergravity requires to construct by hand a supersymmetric extension of the Maxwellian extended Bargmann algebra by introducing additional fermionic and bosonic generators. The new non-relativistic supergravity action presented here contains the extended Bargmann supergravity as a sub-case.

We explore the possibility of finding pure Lovelock gravity as a particular limit of a Chern-Simons action for a specific expansion of the AdS algebra in odd dimensions. We derive in detail this relation at the level of the action in five and seven dimensions. We provide a general result for higher dimensions and discuss some issues arising from the obtained dynamics.